Cylindrical /1-helix model

Fig. 14. Cylindrical /1-helix model of polyglutamine fibrils, from Perutz et at. (2002a).

Its structure was characterized by small-angle X-ray scattering (SAXS) (Fig. 7a). In Fig. 7a, three SAXS profiles are presented. Two of them are calculated theoretically (lines 1,2) and the third profile (open circles) represents experimental results. Both lines 1 and 2 are obtained using the model of a kinked cylindrical helix as imaged in Fig. 7b. For fine 2, the partial aggregation of the helices is taken into account. The theoretical and experimental... 

A flexible helix model in which the surfactant molecules form a flexible cylindrical micelle and the polypeptide chain of the protein wraps around it and is stabilized by hydrogen bonding between the surfactant head group and the peptide bond nitrogen atoms. 

Figure 3.S Schematic diagram of packing side chains In the hydrophobic core of colled-coll structures according to the "knobs In holes" model. The positions of the side chains along the surface of the cylindrical a helix Is pro-jected onto a plane parallel with the heUcal axis for both a helices of the coiled-coil. (a) Projected positions of side chains in helix 1. (b) Projected positions of side chains in helix 2. (c) Superposition of (a) and (b) using the relative orientation of the helices In the coiled-coil structure. The side-chain positions of the first helix, the "knobs," superimpose between the side-chain positions In the second helix, the "holes." The green shading outlines a d-resldue (leucine) from helix 1 surrounded by four side chains from helix 2, and the brown shading outlines an a-resldue (usually hydrophobic) from helix 1 surrounded by four side chains from helix 2.

It has been suggested that the Sup35p filament may be a bundle of four cylindrical //-sheets or nanotubes (Kishimoto et al., 2004). The nanotube is a hypothetical structure (Perutz et al, 2002) whose winding of the polypeptide chain is topologically similar to that of a //-helix but it is round in cross section and water filled whereas //-helices have cross sections with triangular or other shapes and water is largely excluded from their interiors (Kajava and Steven, 2006). The model of Kishimoto et al. envisaged six coils... 

A) Ribbon diagram of an extended polyglutamine sequence forming a cylindrical, parallel /1-helix. The sequence forms a continuous /1-strand, although the peptide whose diffraction served as the basis for the model would only make up one coil. 

The initial experiences with polyisocyanides, especially solubilities and some Debye-Scherrer X-ray data (3), and an consideration of the most probable molecular structure (4), led to an early tentative conclusion that poly(a-phenyl-ethyl isocyanide) and poly(conformational model of a tightly wound helix with an overall shape of a cylindrical rod of about 15 A diameter (3). 

In 1961 a molecular model of a (7/2) helix [Figure 6(a)] was proposed by the author and his coworkers (13.) based on the information from x-ray, infrared, and Raman spectroscopy, but the crystal structure could not be determined at that time. After ten years, owing to the development of methods and apparatus, especially the constrained least-squares method and a vacuum cylindrical camera with a radius of 10 cm, the crystal structure has been determined as shown in Figure 6(c) (22.). The internal rotation angles are considerably distorted from the uniform helix, although the molecular conformation is essentially the (7/2) helix and close to the TTG sequences. 

Figure 15. Cylindrically averaged transforms of the two models illustrated in Figures 6 and 7 (a) intensity distribution on successive layer lines for the triple-stranded 7, helix (b) intensity distribution on successive layer lines for the triple-stranded 6, helix. Note layer lines with index 1 = 1,2, 4, and 5 are absent.

In 2002, Perutz et al. (2002a) proposed an alternative structure for amyloid protofibrils, a water-filled nanotube formed by a polyglutamine protein. This model is a parallel P-helix consisting of an extended polypeptide chain wrapping around a cylindrical terr late, where adjacent strands of the hehx are connected through H-bonds (Fig. 4) and is based on two key features of the polyglutamine diflraction data the absence of a 10-A reflection and the presence of a weak, low-angle reflection of 31 A. 

A perfect helical main chain conformation always leads to a rodlike or cylindrical external shape. But each monomeric unit in such a rod contributes a certain flexibility. So, the flexibility of the rod, as a whole, must increase with increasing degree of polymerization, even when the flexibility per monomeric unit remains constant. A macroscopic example of this would be the flexibility of steel wires of equal diameter but different lengths. Thus, even a perfect helix will adopt coil shape if the molecular mass is very high. Because of this, helically occurring macromolecules, and other stiff macromolecules, can often be well represented by what is known as the wormlike screw model for macromolecular chains at low molecular masses, the chains behave like a stiff rod, but for high molecular masses, the behavior is more coil-like. Examples are nucleic acids, many poly(a-amino acids), and highly tactic poly(a-olefins). 

Fig. 1. Mean helix arc between two neighbour phosphate sites plotted in cylindrical coordinates for the B form of DNA (model 3 of Langridge et al.).

The authors also reported on A-B-A type block copolymers composed of poly(y-benzyl-L-glutamate) as the A component and polyisoprene as the B component. By using wide-angle X-ray diffraction it could be shown that the block copolymers exhibit mesophase behavior in different solvents. In this case polyisoprene chains are in a random coil conformation and form domains embedded in the matrix phase consisting of poly(y-benzyl-L-glutamate) chains in the a-helix conformation. Model analysis of the complex modulus of the membrane cast from solution suggested the occurrence of spherical and cylindrical domain structures in the membrane [73]. Morphological study of these triblock copolymers... 

---